A Fast k Nearest Neighbor Finding Algorithm Based on the Ordered Partition

We propose a fast nearest neighbor finding algorithm, named tentatively an ordered partition, based on the ordered lists of the training samples of each projection axis. The ordered partition contains two properties, one is ordering-to bound the search region, and the other is partitioning-to reject the unwanted samples without actual distance computations. It is proved that the proposed algorithm can find k nearest neighbors in a constant expected time. Simulations show that the algorithm is rather distribution free, and only 4.6 distance calculations, on the average, were required to find a nearest neighbor among 10 000 samples drawn from a bivariate normal distribution.